data2 = {{0, 0}, {0.005508646549712282`,
0.24025544035484173`}, {0.0071667362823842895`,
0.45698565257787205`}, {0.008671448772390455`,
0.6855975985691704`}, {0.010494297126023733`,
0.9226547829206518`}}
FindFit[data2, {BetaRegularized[x, a, b], a > 1 && b > 1}, {a, b},
x] // Timing
It takes half a second for 5 datapoints, and seems to grow in linear
proportion to the size of data, so for full dataset it takes more than
couple of minutes. On other hand if I fit some other function like Erf
in it's place, it takes seconds.
Full dataset
http://yaroslavvb.com/research/ideas/hmms/slow-beta/slow-beta.nb